pC02 (bar)

Figure 13,5. Global mean surface temperature as a function of atmospheric CO? and CH» concentrations, as calculated with a radiative-convective climate model. The solar flux is assumed to be 80% of its present value. The dotted curve represents the upper limit on pCOj obtained from palcosols (Rye ct aL, 1995). (After Pavlov el al., 1999.)

show calculated mean surface temperatures at 2.8 Ga for different amountsofCH4 and CO?. According to liquation (1), the solar flux was about 80% of its present value at that time. The dashed line shows the freezing temperature of water, and the dotted curve represents the upper limit on CO? derived from palcosols (Rye et aE, 1995). The figure shows that, for a methane-free atmosphere, the amount of CO? required to keep the surface temperature above freezing is considerably higher than the limit imposed by the paieosol data. For fltClii) greater than a few times ID"4, however, the disagreement disappears. For example, an atmosphere with f(CH4) — 3 x 10~3 - the concentration predicted for the present-day methane production rate - could have maintained a mean surface temperature within a few degrees of the present value, 288 R, even if atmospheric CO? concentrations were no higher than today.

I conclude that, if methane was abundant in the Archean atmosphere, CO2 eventrations may have been well below those shown in Figure 13.3. Indeed, the silicate-weathering feedback should have worked to ensure this: high CH4 concentrations should have led to warmer surface temperatures, which in turn should have led to faster rates of silicate weathering and increased loss of CO?-

I should add one caveat and one corollary. The caveat is this: Photochemical modeling suggests that methane can be polymerized to higher hydrocarbons, forming Titanlike smog, when the C/O ratio in the atmosphere is greater than ^ I (Zahnle, 1986; Brown, 1999). For the atmospheres discussed here, this condition is equivalent to having f(CH4)/f(CO?) > 1. Thus, the calculations shown in the upper left of Figure 13.5, which do not account for the presence of such haze, may not be realistic. The presence of such a haze would have affected Archean climate both by absorbing incoming solar radiation and by increasing the magnitude of the greenhouse effect (Sagan and Ch vba, 1997), To determine what the net effect on surface temperature would have been requires detailed modeling*

the poles to remain ice-free at the same time that the Tropics were glaciated. (At obliquities above —54 , the equator receives less annually averaged solar insolation than do the poles [Ward, 1974 ).) This avoids the main problem with the snowball Earth h\ poth esis, namely, explaining how life could have made it through such a catastrophe. W ith that thought in mind, mv student Darren Williams performed a series of calculations to see whether it is conceivable that Earth's obliquity could have changed (Williams et al., 1998). The one physical mechanism that might have caused this to happen is so-called "climate friction" - the feedback between Earth's obliquity and its oblateness (Rubincam, 1993; Bills, 1994). Earth's oblateness changes as ice accumulates at the poles, or at the equator during a postulated high-obliquity phase. If this happens in a particular phase relationship with Earths normal 2.5 obliquity oscillation, then the obliquity can gradually drift toward either higher or lower values. We found that if the retreat of the ice lagged the peak solar insolation by less than —20 or more than —200 , the obliquity change could be negative, that is, in the proper direction needed to make George Williams's hypothesis work. Such an obliquity change could also explain the 5 inclination of the lunar orbit with respect to the ecliptic plane, which has been a thorn in the side of celestial mechanicians for many years (Goldreich, 1966; Rubincam, 1975). Since the time our calculations were performed, however, a new theory has been put forward that may explain the Moon's orbit (Touma and \\ isdom, 1998). Inasmuch as it is also difficult to imagine why the phase lag should be so long in the climate friction mechanism, I now consider the high-obliquity hypothesis to he rather improbable. It remains, however, as one conceivable alternative to the theory outlined next.

13.5 The Snowball Earth Hypothesis

A third way of explaining the evidence for low-latitude glaciation is the snow ball Earth hypothesis. This idea has been around for some time (Kirshvink, 1992), but it has gained new credibility from the recent study by Hoffman et al. (1998). Despite assertions to the contrary (Jenkins and Scotese, 1998), there is no reason why global glaciation could not have occurred. If the polar ice sheets were ever to have advanced far enough equatorward, Earth's albedo would have become very high, and freezing of the remaining parts of the ocean is to be expected. This point is illustrated by energv-balance climate model calculations by Caldeira and Kasting (1992) (Figure 13,6). In this type of climate model, the equator-to-pole temperature gradient is simulated by parameterizing latitudinal heat transport by the atmosphere and oceans in the form of a diffusion equation, with a diffusion coefficient chosen to match present-day conditions. The solid curves in Figure 13.6 represent stable solutions for the sine of the ice-line latitude in this model, whereas dashed curves represent unstable solutions. Inspection of the rightmost curve, for pCO^ = 3 x 10 4 bar (the present value), shows that the ice line is unstable for latitudes less than —30 (sine latitude =0.5). If the ice line moves equatorward of this point, it will advance to the stable, completely ice-covered solution at the bottom of the diagram. The critical latitude at which the instability sets in depends on the details of the climate model, in particular the assumed albedo of snow and sea ice (0.66 in the Caldeira and Kasting model). Crowley and Baum's (1993) climate model

Figure 13.6, Ice-line latitude as a function of solar flux and atmospheric CO> level, as calculated by an energy-balance climate model, The solid curves represent stable solutions; dashed curves represent unstable solutions (After Caldcira and Kasting, 1992,)

Effective solar flux {Sefl}

Figure 13.6, Ice-line latitude as a function of solar flux and atmospheric CO> level, as calculated by an energy-balance climate model, The solid curves represent stable solutions; dashed curves represent unstable solutions (After Caldcira and Kasting, 1992,)

is apparently stable with ice sheets down to 25°, but it, too, should become unstable at some point, given similar assumptions about the high albedo of snow and ice.

Global glaciation can be reversed by the build-up of CO2 in Earth's atmosphere. According to Figure 13.6, an accumulation of I). 12 bars of CO? would cause the climate system to revert to an ice-free state, given present solar luminosity. Somewhat higher CO? levels might have been required during the Late Precambrian, when the solar flux was only ~94% of its present value (Equation 1). At a CO2 outgassing rate of 8 x 1012 mol/yr (Holland, 1978), 0.12 bars of C02 could accumulate in million years, assuming no transfer of CO2 between the atmosphere and oceans. Considerably higher atmospheric CO2 concentrations might have been required to reverse the early Proterozoic glaciation, when solar luminosity was only 84% of its present value. Indeed, Caldcira and Kasting( 1992} predicted that global glaciation might have been irreversible during the first part of Earth history because of the formation of CO? ice clouds. This prediction now appears to have been incorrect, though, because such clouds should warm the surface, rather than cool it (Forget and Pierrehumbert, 1997).

The preceding discussion begs the question of how global glaciation could have been triggered in the first place, given the negative feedback on climate provided by the carbonate-silicate cycle. The reason it could have happened is that the ocean surface can freeze much faster than the atmospheric CO2 level can respond to it. A simple calculation using Equation 2 show s that if the planetary albedo were increased from 0.3 to 0.6 (its approximate value in the Caldcira and Kasting snowball Earth model), the planetary energy deficit would be suf ficient to freeze the topmost kilometer of the oceans within less than a thousand years. Thus, what could have happened in the Late Preeambrian is thai the polar ice sheets crept slowly down toward the critical latitude as a consequence of a gradual drawdown of atmospheric CO?. The drawdown might have been caused by supercontinent breakup and a concomitant increase in organic carbon burial on newly created continental shelves, as suggested by Hoffman et al. (1998). Perhaps a better explanation, though, is the suggestion by Marshall et al. (1988): clustering of the continents near the equator allowed silicate weathering to proceed in spite of a generally cold global climate. CX)> was drawn down very low, perhaps near present-day concentrations, and the polar ice caps advanced to the critical latitude. When they reached that point, even a short-lived climatic perturbation, such as a volcanic eruption, could have caused the remaining tropical oceans to freeze over.

What would conditions have been like during such a global glaciation? This is a difficult question and one that deserves consideration because it has important implications for the survival of the biota. If the ice had remained clean, then the planetary albedo should have been MK62 (Caldeira and kasting, 1992), and Equation 2 predicts that Tf = 220 k (compared with 255 K today). At the equator, solar insolation is ~25% higher than the global average, but even there Te would have been only ~23<) K. The atmospheric greenhouse effect was, if anything, smaller than today because of the lower amount of water vapor I shall be generous and assume it was 25 k. Then, even at the equator, the mean annual surface temperature was only '—255 k. The thickness of the ice covering the oceans would have been limited by the geothermal heat flux (M).06 W/irr), w hich would have had to escape through the ice by conduction (Bada et al,, 1994), The conductive heat tlux, in turn, is

As where X( = 2 W/m/k) is the thermal conductivity of ice, AT is the temperature difference across the ice layer, and Az is its thickness. Assuming that the bottom of the ice was at 271 k (the freezing point of seawater), the ice thickness at the equator should have been ^530 m. Everywhere else, the ice would have been thicker.

Here lies the paradox of the snowball Earth model. How did life make it through such a catastrophe? Haifa kilometer of ice would have been totally opaque to sunlight, so pholosynthetic organisms could not have survived beneath the ice surface. The continents would also have had subfreezing climates, so it is not obvious how life could have survived there. Bacteria (or Archea) that live in subsurface environments such as the Columbia River basalt (Stevens and Mckinley, 1995) or within the mid-ocean ridge vent systems would not even know that the glaciation had occurred, but such organisms are phvlogenetically distinct from most modern forms of life, so it is highly unlikely that life re-evolved from them at this late stage in Earth history.

The solution to this paradox may lie in local, geothermal-rich environments such as Iceland, where heat from Earth's interior is concentrated in a particular area. Iceland itself is basically a piece of the Mid-Atlantic spreading ridge that sticks up above the ocean surface. Photosynthetic organisms may have survived the climate catastrophe by liv ing in warm pools in volcanic areas such as this.

Alternatively, the answer to the paradox may have to do with the cleanness of the ice. After the oceans had frozen over, evaporation would have been shut oil and snow fall over the continents would have dropped to minuscule levels. Ice and snow covering the continents would have been w orn away by ablation, exposing dry, dusty soil underneath.

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14 Physical and Chemical Properties of the Glacial Ocean

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